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Ljusternik-Schnirelman theory in partially ordered Hilbert spaces

Authors: Shujie Li and Zhi-Qiang Wang
Journal: Trans. Amer. Math. Soc. 354 (2002), 3207-3227
MSC (2000): Primary 35J20, 35J25, 58E05
Published electronically: April 3, 2002
MathSciNet review: 1897397
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Abstract: We present several variants of Ljusternik-Schnirelman type theorems in partially ordered Hilbert spaces, which assert the locations of the critical points constructed by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of sign-changing solutions.

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Additional Information

Shujie Li
Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing 100080, P.R. China

Zhi-Qiang Wang
Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322

Keywords: Ljusternik-Schnirelman theory, order structure, minimax method, sign-changing solutions
Received by editor(s): November 1, 2001
Published electronically: April 3, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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